I was in Barcelona for a week last year and it was brilliant.
I would recommend the Gaudi sites unless you have no interest at all in architecture, but If you are planning to visit any of them you really must book a timed ticket in advance, otherwise you will spend a lot of time queueing with no guarantee of getting in. For example at Sagrada Familia I had a ticket for 9.30 Tuesday morning and when I arrived they were telling people in the queue that the earliest tickets still available were for 4.00 in the afternoon. The advantage of the timed tickets is that the sites are not too crowded once you get inside.
With two weeks you should also have time to get out of the city. I would recommend a trip to Montserrat, not for the monastery but for the superb mountain walk accessed by cable car which has great views and is not difficult. Girona to the north east is a fine old town with medieval walls that can easily be reached by train. If you have any interest in Roman remains you could also go to Tarragona to the south west. I didnt get there but it appears there is a lot to see though some of the sites are a bit spread out, including an aqueduct above a valley just out of town.